Skip to content

Canonical Gymnasium Mathematics Residue Control Board

Snapshot: 2026-04-01

Purpose:

  • control the remaining canonical math residue after the first package passes for the main top-level topics
  • prevent random reopening of frozen topic cuts without concrete reviewed-state pressure
  • make explicit which residues are
  • accepted as source-granularity noise
  • waiting for more reviewed-state evidence
  • strong enough to justify reopening a canonical package split

Working rule:

  1. do not reopen a frozen topic package just because one broad source corridor feels imperfect
  2. classify each residue explicitly
  3. only reopen a canonical cut if multiple reviewed lanes or a hard runtime/validation problem force it
  4. otherwise prefer
  5. state-local parent remaps
  6. clearer broad-parent placement
  7. explicit documentation that the residue is source granularity, not a canonical gap

Legend:

  • accept: reviewed and accepted as source granularity or stable packaging residue
  • watch: real tension exists, but not enough reviewed pressure to reopen yet
  • reopen-if-forced: next contradictory reviewed lane should reopen the package cut
  • next-lane: more reviewed-state evidence is the right next step

Residue board

Residue Topic Scope Status Current judgment Next action
AN5-late-continuation Sek II Analysis canonical + BB/BE/HB/HH/HE/NI accept the reviewed NI upper-secondary lane adds explicit differential-equation continuation and parameter-family evidence, but these already land on distinct canonical atoms without forcing a new visible AN5 package keep the current AN2-AN4 surface frozen and reopen only if another reviewed lane shows a shared late continuation gap that cannot be absorbed by the existing atomic targets
ST3-HH-Modul-5.2 Sek II Stochastik HH accept Modul 5.2 Hypothesentests und Normalverteilung is a real source hybrid, but child mappings already separate ST3 and ST4 cleanly enough keep broad parent placement and do not invent a new canonical bridge package from this alone
AGV-HH-Modul-6-parent Sek II Analytische Geometrie / Vektoren HH + BB/BE/BY/SH accept the broad HH Modul 6 parent still sits above tighter AGV4/AGV5 children, but BB, BE, BY, and SH reviewed upper-secondary lanes now fit the frozen AGV surface without forcing an extra bridge package keep the current AGV package cut frozen and only reopen if another reviewed state shows the same late relation/metric hybrid pattern at parent level
LM5-role Sek II Lineare Algebra / Matrizen canonical + BB/BE/BY/NI accept BE fits the frozen LM2-LM4 surface cleanly, BY now adds a first reviewed LM2-LM4 parent pass on the same frozen surface, BB contributes the first exact projection-intuition side lane, and the reviewed NI lane adds explicit matrix-based projection evidence that lands directly on the late LM5 continuation keep the current LM2-LM5 package cut frozen and reopen only if another reviewed lane exposes a real shared gap between transition-matrix work and geometric mapping matrices
A5-late-equation-split Sek I Zahlen / Terme / Algebra canonical + HB/HH/HE/SH accept the SH lower-secondary lane adds the missing pressure test: linear systems fit the current A4 surface, while quadratic and exponential equations stay attached to the function-side boundary packages rather than forming one shared late-algebra corridor keep A5 closed for now and reopen only if another reviewed lane exposes a genuinely shared late-algebra continuation outside both A4 and the function packages
F-mixed-lower-secondary-corridors Sek I Funktionen / Zuordnungen HB/HH accept remaining broad lower-secondary corridors still mix algebra and function language, but the shared canonical function surface no longer looks like the main problem keep correcting parent mappings locally instead of reopening the function packages

Current recommendation

Next productive mode:

  1. residue control on frozen topics
  2. additional reviewed-state pressure where the residue board says watch or next-lane

Best next reviewed-state pressure tests:

  1. keep residue control quiet until a validator finding or a new reviewed lane creates concrete package pressure
  2. reopen a frozen topic only when the new evidence cannot be absorbed by parent remaps or existing atomic targets

Reason:

  • the upper-secondary package surfaces for analysis, stochastics, analytic geometry, and matrices now exist
  • AGV now has additional reviewed pressure from BB/BE/BY/SH without reopening the package cut
  • LM now has additional reviewed pressure from BB/BE/BY without forcing a package split or remap wave
  • A5 is now pressure-tested by SH and does not need to be opened as a visible package
  • the main remaining uncertainty is no longer first package invention but the remaining watch residues